
Here, \(\mathrm {B}(\mu ,\sigma )\)  is a beta function with shape parameters \(\alpha _{\chi }\) , \(\beta _{\chi }\) , which corresponds to a mean \(0.67\)  and standard deviation \(0.1\)  [1]}, [2]}, [3]}.
We assume that the 1G+2G  and 2G+2G  spins are isotropically oriented, the same as for 1G+1G  binaries.
